Atkin-Lehner |
7- 11- 23- |
Signs for the Atkin-Lehner involutions |
Class |
12397p |
Isogeny class |
Conductor |
12397 |
Conductor |
∏ cp |
14 |
Product of Tamagawa factors cp |
deg |
163072 |
Modular degree for the optimal curve |
Δ |
18086685721743331 = 79 · 117 · 23 |
Discriminant |
Eigenvalues |
-1 3 3 7- 11- 1 6 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-70251,-3063896] |
[a1,a2,a3,a4,a6] |
j |
950152003191/448204933 |
j-invariant |
L |
4.2989488017295 |
L(r)(E,1)/r! |
Ω |
0.30706777155211 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
111573r1 12397q1 |
Quadratic twists by: -3 -7 |